Can I make a bevel curve transition to another one during the same bevel process?
I don't know of a way to to morph a bevel from one curve to another.  If you want a blend a curved plane from one profile to another you need a NURBS surface.




Add (Shift + A) a Surface, NURBS Curve.
Edit the curve to the profile you want for one end of the surface.
Duplicate (Shift + D) the curve and move it along the Y-axis.
Flatten out the curve control point by scaling them in the Z-axis.
Select both curves and press F to loft them into a surface.